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Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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Counting on Letters

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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Teddy Town

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Weekly Problem 31 - 2007

Stage: 3 Challenge Level: Challenge Level:1

Why do this problem?

This problem offers a good opportunity for students to work systematically.

Possible approach

This is a good starter question to have on the board as students enter the room.

Key questions

  • What numbers might go next to the 12?
  • How many ways of putting the numbers on the clock might there be?

Possible extension

  • Can the numbers 1 - 13 be arranged in a circle so that the pairs add up to a triangle number?

Possible support


This problem is taken from the UKMT Mathematical Challenges.

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